1. The problem statement, all variables and given/known data Find the path of a heat-seeking particle placed at (4,3,10) with a temperature field [tex]T(x,y,z) = 400 - 2x^2 - y^2 -4z^2[/tex] 2. Relevant equations Formulas for directional derivative and gradient. 3. The attempt at a solution At any point in space (x,y,z), the particle must be moving in the direction which causes the greatest increase in T. This direction is given by the direction of [tex]\nabla T = < -4x, -2y, -8z > [/tex]. I do not know how to continue from here.